# Bayes' theorem

In probability theory and statistics, **Bayes' theorem** (alternatively **Bayes' law** or **Bayes' rule**; recently **Bayes–Price theorem**[1]^{: 44, 45, 46 and 67 }), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event.[2] For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole.

One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesian statistics.